SL(2,3) in SL(2,5)
This article is about a particular subgroup in a group, up to equivalence of subgroups (i.e., an isomorphism of groups that induces the corresponding isomorphism of subgroups). The subgroup is (up to isomorphism) special linear group:SL(2,3) and the group is (up to isomorphism) special linear group:SL(2,5) (see subgroup structure of special linear group:SL(2,5)).
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Definition
The group is taken as special linear group:SL(2,5): the special linear group of degree two over field:F5.
The subgroup is taken as a representative of the unique conjugacy class of subgroups of order 24. (The conjugacy class contains 5 subgroups).
This subgroup can be obtained explicitly using the quaternionic representation of special linear group:SL(2,3) over field:F5 (see also linear representation theory of special linear group:SL(2,3)).
Arithmetic functions
| Function | Value | Explanation |
|---|---|---|
| order of the whole group | 120 | . See special linear group:SL(2,5) for more. |
| order of the subgroup | 24 | . See special linear group:SL(2,3) for more. |
| index of the subgroup | 5 | |
| size of conjugacy class of subgroup | 5 | |
| number of conjugacy classes in automorphism class | 1 |
